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Question

The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line (12)x=(13)y=(16)z is :

A
1
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B
2
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C
12
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D
4
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Solution

The correct option is A 1
Line parallel to the line x2=y2=z6 and passing through (1,-2, 3) is
x12=y+23=z36=r
A = (2r + 1, 3r – 2, – 6r + 3) is a point on this line.
A lies in the plane x – y + z = 5
2r+13r+26r+3=5r=17A=(97,117,157)
Distance of A from (1, –2, 3) is
(971)2+(117+2)2+(1573)2=174+9+36=77=1


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